A method to analyze the pure bending of tubes of cylindrically anisotropic layers with arbitrary angles including 0° or 90°

2014 ◽  
Vol 109 ◽  
pp. 57-67 ◽  
Author(s):  
Canhui Zhang ◽  
Suong V. Hoa ◽  
Pei Liu
Keyword(s):  
Pure Bending ◽  
Anisotropic Layers ◽  
Cylindrically Anisotropic

A Simple Model for Cornering and Belt-edge Separation in Radial Tires

1986 ◽  
Vol 14 (1) ◽  
pp. 3-32 ◽  
Author(s):  
P. Popper ◽  
C. Miller ◽  
D. L. Filkin ◽  
W. J. Schaffers
Keyword(s):  
Simple Model ◽  
Transverse Shear ◽  
Mathematical Analysis ◽  
Pure Bending ◽  
Radial Tire ◽  
Optimum Angle ◽  
Shear Strains ◽  
Interlaminar Shear ◽  
Edge Separation ◽  
Shear Bending

Abstract A mathematical analysis of radial tire cornering was performed to predict tire deflections and belt-edge separation strains. The model includes the effects of pure bending, transverse shear bending, lateral restraint of the carcass on the belt, and shear displacements between belt and carcass. It also provides a description of the key mechanisms that act during cornering. The inputs include belt and carcass cord properties, cord angle, pressure, rubber properties, and cornering force. Outputs include cornering deflections and interlaminar shear strains. Key relations found between tire parameters and responses were the optimum angle for minimum cornering deflections and its dependence on cord modulus, and the effect of cord angle and modulus on interlaminar shear strains.

The stability of rectangular thin-walled profile with loading according to the scheme of pure bending

2020 ◽  
pp. 41-45
Author(s):  
V.B. Zylev ◽  
◽  
P.O. Platnov ◽  
I.V. Alferov ◽  
◽  
...  
Keyword(s):  
Pure Bending ◽  
Thin Walled ◽  
The Stability

Cylindrically Anisotropic Tubes Containing a Line Dislocation

2006 ◽  
Author(s):  
Chung-Hao Wang
Keyword(s):  
State Space ◽  
Dislocation Line ◽  
Longitudinal Axis ◽  
The State ◽  
Fourier Series Expansion ◽  
General Solutions ◽  
Mixed Dislocation ◽  
Line Dislocation ◽  
Space Formulation ◽  
Cylindrically Anisotropic

An analytical solution of the problem of a cylindrically anisotropic tube which contains a line dislocation is presented in this study. The state space formulation in conjunction with the eigenstrain theory is proved to be a feasible and systematic methodology to analyze a tube with the existence of dislocations. The state space formulation which expediently groups the displacements and the cylindrical surface traction can construct a governing differential matrix equation. By using Fourier series expansion and the well developed theory of matrix algebra, the asymmetrical solutions are not only explicit but also compact in form. The dislocation considered in this study is a kind of mixed dislocation which is the combination of edge dislocations and a screw dislocation and the dislocation line is parallel to the longitudinal axis of the tube. The degeneracy of the eigen relation and the technique to determine the inverse of a singular matrix are thoroughly discussed, so that the general solutions can be applied to the case of isotropic tubes, which is one of the novel features of this research. The results of isotropic problems, which are belong to the general solutions, are compared with the well-established expressions in the literature. The satisfied correspondences of these comparisons indicate the validness of this study. A cylindrically orthotropic tube is also investigated as an example and the numerical results for the displacements and tangential stress on the outer surface are displayed. The effects on surface stresses due to the existence of a dislocation appear to have a characteristic of localized phenomenon.

scholarly journals Comparison of Quantitative Morphology of Layered and Arbitrary Patterns: Contrary to Visual Perception, Binary Arbitrary Patterns Are Layered from a Structural Point of View

2021 ◽  
Vol 11 (14) ◽  
pp. 6300
Author(s):  
Igor Smolyar ◽  
Daniel Smolyar
Keyword(s):  
Boolean Function ◽  
Layer Structure ◽  
Central Element ◽  
Morphological Characteristics ◽  
Building Blocks ◽  
Point Of View ◽  
Living Systems ◽  
Seismic Profiles ◽  
Contour Maps ◽  
Anisotropic Layers

Patterns found among both living systems, such as fish scales, bones, and tree rings, and non-living systems, such as terrestrial and extraterrestrial dunes, microstructures of alloys, and geological seismic profiles, are comprised of anisotropic layers of different thicknesses and lengths. These layered patterns form a record of internal and external factors that regulate pattern formation in their various systems, making it potentially possible to recognize events in the formation history of these systems. In our previous work, we developed an empirical model (EM) of anisotropic layered patterns using an N-partite graph, denoted as G(N), and a Boolean function to formalize the layer structure. The concept of isotropic and anisotropic layers was presented and described in terms of the G(N) and Boolean function. The central element of the present work is the justification that arbitrary binary patterns are made up of such layers. It has been shown that within the frame of the proposed model, it is the isotropic and anisotropic layers themselves that are the building blocks of binary layered and arbitrary patterns; pixels play no role. This is why the EM can be used to describe the morphological characteristics of such patterns. We present the parameters disorder of layer structure, disorder of layer size, and pattern complexity to describe the degree of deviation of the structure and size of an arbitrary anisotropic pattern being studied from the structure and size of a layered isotropic analog. Experiments with arbitrary patterns, such as regular geometric figures, convex and concave polygons, contour maps, the shape of island coastlines, river meanders, historic texts, and artistic drawings are presented to illustrate the spectrum of problems that it may be possible to solve by applying the EM. The differences and similarities between the proposed and existing morphological characteristics of patterns has been discussed, as well as the pros and cons of the suggested method.

Comparison study of crack propagation in rubberized and conventional prestressed concrete sleepers using digital image correlation

2021 ◽  
pp. 095440972110205
Author(s):  
Guoqing Jing ◽  
Du yunchang ◽  
Ruilin You ◽  
Mohammad Siahkouhi
Keyword(s):  
Digital Image Correlation ◽  
Digital Image ◽  
Prestressed Concrete ◽  
Mouth Opening ◽  
Image Correlation ◽  
Crack Mouth Opening Displacement ◽  
Experimental Program ◽  
Pure Bending ◽  
Opening Displacement ◽  
Rubber Concrete

Rubber concrete (RC) has been confirmed to be suitable for concrete sleeper production. This paper studies the cracking behaviour of conventional and rubber-reinforced concrete sleepers based on the results of an experimental program. The cracking behaviour in the pure bending zone was analysed up to a load of 140 kN. The crack mouth opening displacement (CMOD) was accordingly measured using a digital image correlation (DIC) method. The DIC results show that the rubber prestressed concrete sleeper (RPCS) has a resistance against crack initiation that is 20% greater than that of the conventional prestressed concrete sleeper (CPCS) under the same loading condition; however, due to the higher crack growth rate of the RPCS, the first crack detected by the operator forms at 60 kN, which corresponds to a strength approximately 9% lower compared with the 65 kN load at which the first crack is detected in the CPCS. Before the first crack (60 kN), the RPCS has a deflection 35% lower than that of the CPCS, but after cracking, at loads of 80 kN, 100 kN and 140 kN, the RPCS has a deflection 15%, 4% and 24% higher than that of the CPCS, respectively.

Dynamic Fracture of a Beam or Plate in Plane Bending

1976 ◽  
Vol 43 (1) ◽  
pp. 112-116 ◽  
Author(s):  
L. B. Freund ◽  
G. Herrmann
Keyword(s):  
Crack Length ◽  
Dynamic Fracture ◽  
Crack Tip ◽  
Bending Moment ◽  
Fracture Initiation ◽  
Fracture Plane ◽  
Multiple Reflections ◽  
Pure Bending ◽  
Strain Fracture ◽  
Beam Thickness

The dynamic fracture response of a long beam of brittle elastic material subjected to pure bending is studied. If the magnitude of the applied bending moment is increased to a critical value, a crack will propagate from the tensile side of the beam across a cross section. An analysis is presented by means of which the crack length and bending moment at the fracturing section are determined as functions of time after fracture initiation. The main assumption on which the analysis rests is that, due to multiple reflections of stress waves across the thickness of the beam, the stress distribution on the prospective fracture plane ahead of the crack may be adequately approximated by the static distribution appropriate for the instantaneous crack length and net section bending moment. The results of numerical calculations are shown in graphs of crack length, crack tip speed, and fracturing section bending moment versus time. It is found that the crack tip accelerates very quickly to a speed near the characteristic terminal speed for the material, travels at this speed through most of the beam thickness, and then rapidly decelerates in the final stage of the process. The results also apply for plane strain fracture of a plate in pure bending provided that the value of the elastic modulus is appropriately modified.

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